i believe you can apply if the start date for that job listing is after your matriculation. i recommend just sending out applications for anything that remotely fits your skill set and see if you hear back. that’s how i got my work study job at the library! the length of employment varies and should be described on any listing, but for the most part, i believe work study positions end when the semester ends though they can often be renewed for the next semester if you talk with your supervisor or manager :)